At the end of the film where Nick shoots his brother Conrad who then plays possum at the roof, how'd Conrad manage to reach the gala hall during Nick's jump?
It probably took a few minutes for the paramedics to check Nicholas over after his landing, and the time is justifiably compressed because he's so disoriented. Not long, but long enough for Conrad to stop playing possum and rush down via express elevator.
If the gunshots were all blanks and squibs, then how the tire on the (fake) private investigator's car get blown out by the gunshot? They would have had to known in advance that (a)Nicholas Van Orton would have confronted the private investigator (b)he would have stolen the gun (c)he would have shot the gun and (d)he would have shot it at the tire.
They could've just guessed he might do that. The PI could've been wearing a squib shirt too. The point is, it was entirely optional. It wasn't necessary to that scene that he take the gun and shoot anything, just that he think someone had sent a PI after him.
Indeed, they probably had all four tires rigged to blow if necessary, and probably set up all the windows and side mirrors to break on cue as well. If he'd shot at part of the car that wasn't pre-rigged, like the body of the vehicle, they'd blow the nearest squib to where he was aiming and pretend he'd just missed his exact target.
Perhaps the gun was loaded with live rounds. They would not have expected Van Orton to actually shoot someone, and he didn't.
If the gunshots were all blanks and squibs, then how did the car window get bullet holes in it?
You answered your own question, blanks are what makes the muzzle flash from the gun, and squibs are the bullet "hits". They likely used the exact same method as a movie shoot would.
How did they know what part of the building he would jump from?
It's a bit of a stretch, but Feingold mentions that if he hadn't jumped at all, he was supposed to throw him off. If Nick had wandered toward the wrong part of the roof in a suicidal daze — and they had enough of his actions planned already — he probably could have caught him and gotten him back on the rails.
On a related note, what if he'd not bothered to jump and shot himself on the spot instead? Even a blank can kill if it's fired with the gun's muzzle set directly against the skull.